As such there's no difference but I have noticed that people come across some problem, error when installing via online using onlinesetup installer, maybe due to slow net connections etc. Also the offline installer comes in handy when you face any error, just uninstall and run the offline installer again to reinstall any corrupt,missing files without connecting to net.
I have always preferred offline installer and I download and keep it, though its >200MB.

I had WLPG working after using the offline installer, but I am now getting the 0x8007002 error again. The problem is aggravated by the fact that although I have WLPG and Windows Live Mail installed neither of them (or Windows Live Essentials) appear on my Add/Remove programs list, so I have not got the usual options of either repair or uninstall.

OK, so I think the problem is being caused by earlier installs and incomplete/corrupt removal of Essentials.
So let us first remove it completely manually.
Pl follow these steps to uninstall -
From Start > type in search box
%programfiles%\Windows Live\Installer
and press enter to open up that folder.
Double click on wlarp.exe and clcik on 'Remove one or more Windows Live programs'
and select everything and uninstall all following the instructions.
If you could uninstall everything without any error, Live Essentials is removed successfully. Restart and install again with your offline installer.

I hope your Windows 7 is upto date with all its updates else update it.